Preheat the oven to 425 degrees F. Make the croutons: Toss the bread cubes with 1 tablespoon olive oil on a rimmed baking sheet; season with salt and pepper. Bake until golden, about 8 minutes.
Meanwhile, make the dressing: Heat the remaining 1/3 cup olive oil in a medium skillet over medium heat. Add the shallot and tomatoes and cook until softened, about 5 minutes. Stir in the lemon juice and season with salt and pepper.
Toss the lettuce in a large bowl. Pour the warm dressing on top, add the croutons and gently toss. Top with the blue cheese.